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by FabHK 3413 days ago
Yes, that rule:

   31%  outside +/- 1 standard deviation  ("2 sigma"), 
   5%   outside +/- 2 standard deviations ("4 sigma"),
   0.3% outside +/- 3 standard deviations ("6 sigma"), 
etc. However, the more general Chebyshev inequality states that for any distribution, you have at most 1/k^2 outside +/- k standard deviations, so (at most):

   100% outside +/- 1 standard deviation, 
    25% outside +/- 2 standard deviations,
     9% outside +/- 3 standard deviations, 
etc.

https://en.wikipedia.org/wiki/Chebyshev%27s_inequality